When BLE meets MEMS: The basics of inertial systems

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When BLE meets MEMS: The basics of inertial systems [Copy link]

 

Let's introduce some basic knowledge of inertial systems and learn step by step by asking questions.

1. What are MEMS, IMU, and strapdown?

MEMS is called Micro-Electro-Mechanical System (MEMS). Common MEMS products include accelerometers, microphones, micromotors, optical sensors, pressure sensors, gyroscopes, humidity sensors, etc.

IMU is called Inertial Measurement Unit, which is a device for measuring the three-axis attitude angle (or angular rate) and acceleration of an object. Gyroscopes and accelerometers are the main components of IMU.

The original meaning of the term "Strapdown" in English is "binding". Therefore, the so-called strapdown inertial system is to "bind" the inertial sensitive components (gyroscopes and accelerometers) directly to the body of the carrier.

So the IMUs with MEMS structures that we buy now are all strapdown inertial systems.

2. What is a coordinate system?

The function of coordinates is to determine the position and other information of a point. In life, we often use various coordinates without knowing it. For example, "the sun rises in the east and sets in the west," the reference coordinate system is the geodetic coordinate system. "My left," the reference coordinate system is the body coordinate.

3. How to describe moving forward? ——Body coordinates

Body coordinates are fixedly connected to objects. The three axes XYZ can be defined by themselves and must comply with the right-hand rule. For the convenience of understanding, we use people as objects here and define the center point of the human body as point B. Define the top of the head as the BZ axis, the front as the BY axis, and the right as the BX axis, then the body coordinate system is established. To describe forward movement, we can say that it moves in the positive direction of the BY axis of the body coordinate system.

4. How to describe going west? ——Ground coordinate system

The ground coordinates usually refer to the ground coordinate system, which defines a point on the surface of the earth as point E, and the EX axis as an arbitrary direction pointing to the ground plane. The EZ axis is vertically upward, and the plane formed by the EY and EZ axes is perpendicular, forming a right-handed coordinate system. Here we define the EX axis to point to the west, so the EY axis points to the south, and the EZ axis points to the sky. Then this ground coordinate system is established. It is best if the ground coordinate system defined here can coincide with the body coordinate direction. For example, if a person stands facing south, the body coordinates coincide with the ground coordinate system. To describe westward movement, we can say that it moves in the positive direction of the EX axis of the ground coordinate system.

5. How to describe turning in a circle? ——Euler angles

If we rotate 90 degrees with the BZ axis as the axis, we cannot do it with the above coordinates. Because the direction of rotation is not defined first, that is, whether 90 degrees should be rotated clockwise or counterclockwise, and it is also not defined which coordinate system the 90 degrees refers to. Because the body coordinates are always fixed to the object, they will rotate when you rotate them. At this time, a reference body coordinate system is needed (the origin of the coordinates is the origin of the body coordinates, which does not rotate with the object), and it is also necessary to define which direction is positive.

Now let's define the axis of the coordinate axis projecting out of the paper as the counterclockwise rotation is positive. That is, counterclockwise rotation is positive rotation around the Z axis, lying down is positive rotation around the X axis, and falling to the right is positive rotation around the Y axis. For example, in the figure, the X axis rotates to X', the Z axis rotates to Z', and the Y axis does not move. The resulting angle is the angle of θ clockwise rotation with the Y axis as the center. This solves the problem of rotation. The reference body coordinate system is used as the standard for the number of degrees of rotation. To describe a 90-degree counterclockwise rotation with the body as the axis, that is, a 90-degree counterclockwise rotation with the Z axis as the axis, but it is too troublesome to describe the rotation like this every time, so the Euler angle is generated.

Refer to the figure above and set the xyz-axis as the reference axis of the reference system. The intersection of the xy-plane and the XY-plane is called the intersection line, represented by the English letter (N).

α /'lf/ (or φ/fa/ or yaw) The angle between the x-axis and the N-axis, representing the rotation around the z-axis.

β /'bi:t/ (or θ/'θi:t/ or pitch) The angle between the z-axis and the Z-axis represents the rotation around the N-axis.

γ /'gm/ (or ψ/ps/ or roll) The angle between the N-axis and the X-axis represents the rotation around the Z-axis.

Euler angles are used in navigation to calculate yaw(yaw), pitch(/size), and pitch(/size). olor])androll(roll)description, the picture is as follows:

Then the 90-degree counterclockwise rotation with the body as the axis mentioned above can be said to be α or φ or yaw rotation of 90 degrees.

6. If I walk forward, will I go all the way west? ——Rotation matrix and coordinate transformation

It was introduced earlier that Euler angles can describe the rotation of an object, but there is a problem when there are multiple Euler angles, because the rotation order of the three Euler angles is different, resulting in different results. Here is an example of two actions: 1, rotate 90 degrees in the direction in front of the eyes, 2, rotate 90 degrees counterclockwise with the body as the axis. Doing 1 first and doing 2 first will result in two different postures.

So the following rotation order is usually agreed upon:

1. XYZ rotates around the Z axis (the axis that initially coincides with the Z axis) by an angle of α. Now the X axis is on the intersection line.

2. XYZ rotates around the current X axis by an angle of β. The Z axis is now at its final position, and the X axis is still on the intersection line.

3. XYZ rotates around the new Z axis by an angle of γ.

This is shown in the following animation:

A simple way to generate a rotation matrix is to composite it as a sequence of three basic rotations: roll, pitch and yaw rotations. Because these rotations are expressed as rotations about a single axis, their generators are easy to express.

Multiplying the rotation matrix by a three-row array makes the above expression clear.

Use the above rotation order to multiply

(for α and γ, the range is [π, π], for β,range is[0, π])

We introduced body coordinates and ground coordinates earlier, but if we keep walking forward, which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

π]）

Body coordinates and ground coordinates were introduced earlier, but if we keep walking forward, then which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

π]）

Body coordinates and ground coordinates were introduced earlier, but if we keep walking forward, then which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

π]）

Body coordinates and ground coordinates were introduced earlier, but if we keep walking forward, then which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

π]）

Body coordinates and ground coordinates were introduced earlier, but if we keep walking forward, then which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

XYZ rotates around the Z axis (the axis that initially coincides with the Z axis) by an angle of α. Now the X axis is on the intersection line.

2. XYZ rotates around the current X axis by an angle of β. The Z axis is now at its final position, and the X axis remains on the intersection line.

3. XYZ rotates around the new Z axis by an angle of γ.

This is shown in the following animation:

A simple way to generate a rotation matrix is to composite it as a sequence of three basic rotations: roll, pitch and yaw rotations. Because these rotations are expressed as rotations about a single axis, their generators are easy to express.

Multiplying the rotation matrix by a three-row array makes the above expression clear.

Use the above rotation order to multiply

(for α and γ, the range is [π, π], for β,range is[0, π])

We introduced body coordinates and ground coordinates earlier, but if we keep walking forward, which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

XYZ rotates around the Z axis (the axis that initially coincides with the Z axis) by an angle of α. Now the X axis is on the intersection line.

2. XYZ rotates around the current X axis by an angle of β. The Z axis is now at its final position, and the X axis remains on the intersection line.

3. XYZ rotates around the new Z axis by an angle of γ.

This is shown in the following animation:

A simple way to generate a rotation matrix is to composite it as a sequence of three basic rotations: roll, pitch and yaw rotations. Because these rotations are expressed as rotations about a single axis, their generators are easy to express.

Multiplying the rotation matrix by a three-row array makes the above expression clear.

Use the above rotation order to multiply

(for α and γ, the range is [π, π], for β,range is[0, π])

We introduced body coordinates and ground coordinates earlier, but if we keep walking forward, which direction do we want to go in the ground coordinates? This involves coordinate transformation. Since the body coordinates are fixed on the object, the body coordinates rotate when the object rotates, so there is a rotation relationship between the body coordinates and the ground coordinates. If we know the rotation matrix from body coordinates to ground coordinates, then the direction, speed, and angular velocity in the body coordinates can be obtained by multiplying the rotation matrix by the rotation matrix. This solves the problem of whether I am walking all the way west.

夜违背

Learned  

yzhfx

The picture of the OP is a bit evil

jack4103

Learned

ksniper

yzhfx posted on 2018-10-25 12:02 The picture of the OP is a bit evil

B is in the right place Nothing wrong

lb8820265

ksniper posted on 2018-10-26 10:10 B is fine in the right place

Haha, this is exactly the effect I want. This will make you more focused and more impressed

tianshilande

Wonderful, well explained